A KAM theorem with applications to partial differential equations of higher dimensions

作者：Yuan Xiaoping^*

来源：Communications in Mathematical Physics, 2007, 275(1): 97-137.

DOI：10.1007/s00220-007-0287-2

The existence of lower dimensional KAM tori is shown for a class of nearly integrable Hamiltonian systems of infinite dimensions where the second Melnikov's conditions are completely eliminated and the algebraic structure of the normal frequencies are not needed. As a consequence, it is proved that there exist many invariant tori and thus quasi-periodic solutions for nonlinear wave equations, Schrodinger equations and other equations of any spatial dimensions.

• 出版日期2007-10
• 单位复旦大学